** If compiling for a processor that lacks floating point support,
** substitute integer for floating-point
*/
#ifdef SQLITE_OMIT_FLOATING_POINT
# define double sqlite_int64
# define LONGDOUBLE_TYPE sqlite_int64
# ifndef SQLITE_BIG_DBL
#   define SQLITE_BIG_DBL (((sqlite3_int64)1)<<60)
# endif
# define SQLITE_OMIT_DATETIME_FUNCS 1
# define SQLITE_OMIT_TRACE 1
# undef SQLITE_MIXED_ENDIAN_64BIT_FLOAT
# undef SQLITE_HAVE_ISNAN
#endif
#ifndef SQLITE_BIG_DBL

** If compiling for a processor that lacks floating point support,
** substitute integer for floating-point
*/
#ifdef SQLITE_OMIT_FLOATING_POINT
# define double sqlite_int64
# define LONGDOUBLE_TYPE sqlite_int64
# ifndef SQLITE_BIG_DBL
#   define SQLITE_BIG_DBL (((sqlite3_int64)1)<<50)
# endif
# define SQLITE_OMIT_DATETIME_FUNCS 1
# define SQLITE_OMIT_TRACE 1
# undef SQLITE_MIXED_ENDIAN_64BIT_FLOAT
# undef SQLITE_HAVE_ISNAN
#endif
#ifndef SQLITE_BIG_DBL

    if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){
      double r = sqlite3_value_double(pVal);
      for(i=0; i<SQLITE_INDEX_SAMPLES; i++){
        if( aSample[i].eType==SQLITE_NULL ) continue;
        if( aSample[i].eType>=SQLITE_TEXT || aSample[i].u.r>r ) break;
      }
    }else if( eType==SQLITE_TEXT || eType==SQLITE_BLOB ){
      sqlite3 *db = pParse->db;
      CollSeq *pColl;
      const u8 *z;
      int n;




      if( eType==SQLITE_BLOB ){
        z = (const u8 *)sqlite3_value_blob(pVal);
        pColl = db->pDfltColl;
        assert( pColl->enc==SQLITE_UTF8 );
      }else{
        pColl = sqlite3GetCollSeq(db, SQLITE_UTF8, 0, *pIdx->azColl);
        if( pColl==0 ){
................................................................................
**
**   ... FROM t1 WHERE a > ? AND a < ? ...
**                    |_____|   |_____|
**                       |         |
**                     pLower    pUpper
**
** If the upper or lower bound is not present, then NULL should be passed in
** place of a WhereTerm.
**
** The nEq parameter is passed the index of the index column subject to the
** range constraint. Or, equivalently, the number of equality constraints
** optimized by the proposed index scan. For example, assuming index p is
** on t1(a, b), and the SQL query is:
**
**   ... FROM t1 WHERE a = ? AND b > ? AND b < ? ...
................................................................................
** value of 1 indicates that the proposed range scan is expected to visit
** approximately 1/9 (11%) of the rows selected by the nEq equality constraints
** (if any). A return value of 9 indicates that it is expected that the
** range scan will visit 9/9 (100%) of the rows selected by the equality
** constraints.
*/
static int whereRangeScanEst(
  Parse *pParse,
  Index *p, 
  int nEq, 
  WhereTerm *pLower, 
  WhereTerm *pUpper,
  int *piEst                      /* OUT: Return value */
){
  int rc = SQLITE_OK;

#ifdef SQLITE_ENABLE_STAT2
  sqlite3 *db = pParse->db;
  sqlite3_value *pLowerVal = 0;
  sqlite3_value *pUpperVal = 0;
................................................................................
  WhereCost *pCost            /* Lowest cost query plan */
){
  int iCur = pSrc->iCursor;   /* The cursor of the table to be accessed */
  Index *pProbe;              /* An index we are evaluating */
  Index *pIdx;                /* Copy of pProbe, or zero for IPK index */
  int eqTermMask;             /* Current mask of valid equality operators */
  int idxEqTermMask;          /* Index mask of valid equality operators */

  Index pk;
  unsigned int pkint[2] = {1000000, 1};
  int pkicol = -1;
  int wsFlagMask;

  memset(pCost, 0, sizeof(*pCost));
  pCost->rCost = SQLITE_BIG_DBL;

  /* If the pSrc table is the right table of a LEFT JOIN then we may not
  ** use an index to satisfy IS NULL constraints on that table.  This is
  ** because columns might end up being NULL if the table does not match -
  ** a circumstance which the index cannot help us discover.  Ticket #2177.
................................................................................
  if( pSrc->jointype & JT_LEFT ){
    idxEqTermMask = WO_EQ|WO_IN;
  }else{
    idxEqTermMask = WO_EQ|WO_IN|WO_ISNULL;
  }

  if( pSrc->pIndex ){

    pIdx = pProbe = pSrc->pIndex;
    wsFlagMask = ~(WHERE_ROWID_EQ|WHERE_ROWID_RANGE);
    eqTermMask = idxEqTermMask;
  }else{
    Index *pFirst = pSrc->pTab->pIndex;


    memset(&pk, 0, sizeof(Index));
    pk.nColumn = 1;
    pk.aiColumn = &pkicol;
    pk.aiRowEst = pkint;

    pk.onError = OE_Replace;
    pk.pTable = pSrc->pTab;

    if( pSrc->notIndexed==0 ){
      pk.pNext = pFirst;
    }




    if( pFirst && pFirst->aiRowEst ){

      pkint[0] = pFirst->aiRowEst[0];


    }
    pProbe = &pk;
    wsFlagMask = ~(
        WHERE_COLUMN_IN|WHERE_COLUMN_EQ|WHERE_COLUMN_NULL|WHERE_COLUMN_RANGE
    );
    eqTermMask = WO_EQ|WO_IN;
    pIdx = 0;
  }



  for(; pProbe; pIdx=pProbe=pProbe->pNext){
    const unsigned int * const aiRowEst = pProbe->aiRowEst;
    double cost;                /* Cost of using pProbe */
    double nRow;                /* Estimated number of rows in result set */
    int rev;                    /* True to scan in reverse order */
    int wsFlags = 0;
    Bitmask used = 0;
................................................................................
    **    the sub-select is assumed to return 25 rows for the purposes of 
    **    determining nInMul.
    **
    **  bInEst:  
    **    Set to true if there was at least one "x IN (SELECT ...)" term used 
    **    in determining the value of nInMul.
    **
    **  nBound:  
    **    Set based on whether or not there is a range constraint on the 
    **    (nEq+1)th column of the index. 1 if there is neither an upper or 
    **    lower bound, 3 if there is an upper or lower bound, or 9 if there 
    **    is both an upper and lower bound.
    **
    **  bSort:   
    **    Boolean. True if there is an ORDER BY clause that will require an 
    **    external sort (i.e. scanning the index being evaluated will not 
    **    correctly order records).
    **
    **  bLookup: 
................................................................................
      if( m==0 ){
        wsFlags |= WHERE_IDX_ONLY;
      }else{
        bLookup = 1;
      }
    }

#if 0
    if( bInEst && (nInMul*aiRowEst[nEq])>(aiRowEst[0]/2) ){
      nInMul = aiRowEst[0] / (2 * aiRowEst[nEq]);
    }

    nRow = (double)(aiRowEst[nEq] * nInMul) / nBound;
    cost = (nEq>0) * nInMul * estLog(aiRowEst[0])
         + nRow
         + bSort * nRow * estLog(nRow)
         + bLookup * nRow * estLog(aiRowEst[0]);
#else

    /* The following block calculates nRow and cost for the index scan
    ** in the same way as SQLite versions 3.6.17 and earlier. Some elements
    ** of this calculation are difficult to justify. But using this strategy
    ** works well in practice and causes the test suite to pass.  */
    nRow = (double)(aiRowEst[nEq] * nInMul);
    if( bInEst && nRow*2>aiRowEst[0] ){
      nRow = aiRowEst[0]/2;
      nInMul = nRow / aiRowEst[nEq];
    }





    cost = nRow + nInMul*estLog(aiRowEst[0]);




    nRow = nRow * (double)nBound / 9.0;
    cost = cost * (double)nBound / 9.0;



    if( bSort ){
      cost += cost*estLog(cost);
    }





    if( pIdx && bLookup==0 ){
      cost /= 2;
    }
#endif


    WHERETRACE((
      "tbl=%s idx=%s nEq=%d nInMul=%d nBound=%d bSort=%d bLookup=%d"
      " wsFlags=%d   (nRow=%.2f cost=%.2f)\n",
      pSrc->pTab->zName, (pIdx ? pIdx->zName : "ipk"), 
      nEq, nInMul, nBound, bSort, bLookup, wsFlags, nRow, cost
    ));




    if( (!pIdx || wsFlags) && cost<pCost->rCost ){
      pCost->rCost = cost;
      pCost->nRow = nRow;
      pCost->used = used;
      pCost->plan.wsFlags = (wsFlags&wsFlagMask);
      pCost->plan.nEq = nEq;
      pCost->plan.u.pIdx = pIdx;
    }



    if( pSrc->pIndex ) break;


    wsFlagMask = ~(WHERE_ROWID_EQ|WHERE_ROWID_RANGE);
    eqTermMask = idxEqTermMask;
  }

  /* If there is no ORDER BY clause and the SQLITE_ReverseOrder flag
  ** is set, then reverse the order that the index will be scanned
  ** in. This is used for application testing, to help find cases

    if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){
      double r = sqlite3_value_double(pVal);
      for(i=0; i<SQLITE_INDEX_SAMPLES; i++){
        if( aSample[i].eType==SQLITE_NULL ) continue;
        if( aSample[i].eType>=SQLITE_TEXT || aSample[i].u.r>r ) break;
      }
    }else{ 
      sqlite3 *db = pParse->db;
      CollSeq *pColl;
      const u8 *z;
      int n;

      /* pVal comes from sqlite3ValueFromExpr() so the type cannot be NULL */
      assert( eType==SQLITE_TEXT || eType==SQLITE_BLOB );

      if( eType==SQLITE_BLOB ){
        z = (const u8 *)sqlite3_value_blob(pVal);
        pColl = db->pDfltColl;
        assert( pColl->enc==SQLITE_UTF8 );
      }else{
        pColl = sqlite3GetCollSeq(db, SQLITE_UTF8, 0, *pIdx->azColl);
        if( pColl==0 ){
................................................................................
**
**   ... FROM t1 WHERE a > ? AND a < ? ...
**                    |_____|   |_____|
**                       |         |
**                     pLower    pUpper
**
** If the upper or lower bound is not present, then NULL should be passed in
** place of the corresponding WhereTerm.
**
** The nEq parameter is passed the index of the index column subject to the
** range constraint. Or, equivalently, the number of equality constraints
** optimized by the proposed index scan. For example, assuming index p is
** on t1(a, b), and the SQL query is:
**
**   ... FROM t1 WHERE a = ? AND b > ? AND b < ? ...
................................................................................
** value of 1 indicates that the proposed range scan is expected to visit
** approximately 1/9 (11%) of the rows selected by the nEq equality constraints
** (if any). A return value of 9 indicates that it is expected that the
** range scan will visit 9/9 (100%) of the rows selected by the equality
** constraints.
*/
static int whereRangeScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index containing the range-compared column; "x" */
  int nEq,             /* index into p->aCol[] of the range-compared column */
  WhereTerm *pLower,   /* Lower bound on the range. ex: "x>123" Might be NULL */
  WhereTerm *pUpper,   /* Upper bound on the range. ex: "x<455" Might be NULL */
  int *piEst           /* OUT: Return value */
){
  int rc = SQLITE_OK;

#ifdef SQLITE_ENABLE_STAT2
  sqlite3 *db = pParse->db;
  sqlite3_value *pLowerVal = 0;
  sqlite3_value *pUpperVal = 0;
................................................................................
  WhereCost *pCost            /* Lowest cost query plan */
){
  int iCur = pSrc->iCursor;   /* The cursor of the table to be accessed */
  Index *pProbe;              /* An index we are evaluating */
  Index *pIdx;                /* Copy of pProbe, or zero for IPK index */
  int eqTermMask;             /* Current mask of valid equality operators */
  int idxEqTermMask;          /* Index mask of valid equality operators */
  Index sPk;                  /* A fake index object for the primary key */
  unsigned int aiRowEstPk[2]; /* The aiRowEst[] value for the sPk index */
  int aiColumnPk = -1;        /* The aColumn[] value for the sPk index */
  int wsFlagMask;             /* Allowed flags in pCost->plan.wsFlag */

  /* Initialize the cost to a worst-case value */
  memset(pCost, 0, sizeof(*pCost));
  pCost->rCost = SQLITE_BIG_DBL;

  /* If the pSrc table is the right table of a LEFT JOIN then we may not
  ** use an index to satisfy IS NULL constraints on that table.  This is
  ** because columns might end up being NULL if the table does not match -
  ** a circumstance which the index cannot help us discover.  Ticket #2177.
................................................................................
  if( pSrc->jointype & JT_LEFT ){
    idxEqTermMask = WO_EQ|WO_IN;
  }else{
    idxEqTermMask = WO_EQ|WO_IN|WO_ISNULL;
  }

  if( pSrc->pIndex ){
    /* An INDEXED BY clause specifies a particular index to use */
    pIdx = pProbe = pSrc->pIndex;
    wsFlagMask = ~(WHERE_ROWID_EQ|WHERE_ROWID_RANGE);
    eqTermMask = idxEqTermMask;
  }else{
    /* There is no INDEXED BY clause.  Create a fake Index object to
    ** represent the primary key */
    Index *pFirst;                /* Any other index on the table */
    memset(&sPk, 0, sizeof(Index));
    sPk.nColumn = 1;
    sPk.aiColumn = &aiColumnPk;
    sPk.aiRowEst = aiRowEstPk;
    aiRowEstPk[1] = 1;
    sPk.onError = OE_Replace;
    sPk.pTable = pSrc->pTab;
    pFirst = pSrc->pTab->pIndex;
    if( pSrc->notIndexed==0 ){
      sPk.pNext = pFirst;
    }
    /* The aiRowEstPk[0] is an estimate of the total number of rows in the
    ** table.  Get this information from the ANALYZE information if it is
    ** available.  If not available, assume the table 1 million rows in size.
    */
    if( pFirst ){
      assert( pFirst->aiRowEst!=0 ); /* Allocated together with pFirst */
      aiRowEstPk[0] = pFirst->aiRowEst[0];
    }else{
      aiRowEstPk[0] = 1000000;
    }
    pProbe = &sPk;
    wsFlagMask = ~(
        WHERE_COLUMN_IN|WHERE_COLUMN_EQ|WHERE_COLUMN_NULL|WHERE_COLUMN_RANGE
    );
    eqTermMask = WO_EQ|WO_IN;
    pIdx = 0;
  }

  /* Loop over all indices looking for the best one to use
  */
  for(; pProbe; pIdx=pProbe=pProbe->pNext){
    const unsigned int * const aiRowEst = pProbe->aiRowEst;
    double cost;                /* Cost of using pProbe */
    double nRow;                /* Estimated number of rows in result set */
    int rev;                    /* True to scan in reverse order */
    int wsFlags = 0;
    Bitmask used = 0;
................................................................................
    **    the sub-select is assumed to return 25 rows for the purposes of 
    **    determining nInMul.
    **
    **  bInEst:  
    **    Set to true if there was at least one "x IN (SELECT ...)" term used 
    **    in determining the value of nInMul.
    **
    **  nBound:
    **    An estimate on the amount of the table that must be searched due
    **    to a range constraint.  The value is between 1 and 9 and indicates
    **    9ths of the table.  1 means that about 1/9th of the is searched.
    **    9 indicates that the entire table is searched.
    **
    **  bSort:   
    **    Boolean. True if there is an ORDER BY clause that will require an 
    **    external sort (i.e. scanning the index being evaluated will not 
    **    correctly order records).
    **
    **  bLookup: 
................................................................................
      if( m==0 ){
        wsFlags |= WHERE_IDX_ONLY;
      }else{
        bLookup = 1;
      }
    }

    /**** Begin adding up the cost of using this index (Needs improvements)
    **
    ** Estimate the number of rows of output.  For an IN operator,

    ** do not let the estimate exceed half the rows in the table.
    */










    nRow = (double)(aiRowEst[nEq] * nInMul);
    if( bInEst && nRow*2>aiRowEst[0] ){
      nRow = aiRowEst[0]/2;
      nInMul = nRow / aiRowEst[nEq];
    }

    /* Assume constant cost to access a row and logarithmic cost to
    ** do a binary search.  Hence, the initial cost is the number of output
    ** rows plus log2(table-size) times the number of binary searches.
    */
    cost = nRow + nInMul*estLog(aiRowEst[0]);

    /* Adjust the number of rows and the cost downward to reflect rows
    ** that are excluded by range constraints.
    */
    nRow = nRow * (double)nBound / (double)9;
    cost = cost * (double)nBound / (double)9;

    /* Add in the estimated cost of sorting the result
    */
    if( bSort ){
      cost += cost*estLog(cost);
    }

    /* If all information can be taken directly from the index, we avoid
    ** doing table lookups.  This reduces the cost by half.  (Not really -
    ** this needs to be fixed.)
    */
    if( pIdx && bLookup==0 ){
      cost /= (double)2;
    }

    /**** Cost of using this index has now been computed ****/

    WHERETRACE((
      "tbl=%s idx=%s nEq=%d nInMul=%d nBound=%d bSort=%d bLookup=%d"
      " wsFlags=%d   (nRow=%.2f cost=%.2f)\n",
      pSrc->pTab->zName, (pIdx ? pIdx->zName : "ipk"), 
      nEq, nInMul, nBound, bSort, bLookup, wsFlags, nRow, cost
    ));

    /* If this index is the best we have seen so far, then record this
    ** index and its cost in the pCost structure.
    */
    if( (!pIdx || wsFlags) && cost<pCost->rCost ){
      pCost->rCost = cost;
      pCost->nRow = nRow;
      pCost->used = used;
      pCost->plan.wsFlags = (wsFlags&wsFlagMask);
      pCost->plan.nEq = nEq;
      pCost->plan.u.pIdx = pIdx;
    }

    /* If there was an INDEXED BY clause, then only that one index is
    ** considered. */
    if( pSrc->pIndex ) break;

    /* Reset masks for the next index in the loop */
    wsFlagMask = ~(WHERE_ROWID_EQ|WHERE_ROWID_RANGE);
    eqTermMask = idxEqTermMask;
  }

  /* If there is no ORDER BY clause and the SQLITE_ReverseOrder flag
  ** is set, then reverse the order that the index will be scanned
  ** in. This is used for application testing, to help find cases